Hamiltonian Thermodynamics of Charged Black Holes

TL;DR

This paper develops a Hamiltonian framework for charged black holes in 1+1 dimensions, incorporating a topological term, and analyzes the thermodynamics of Reissner-Nordstrom and BTZ black holes.

Contribution

It introduces a new topological term in the action and derives the Hamiltonian partition function for charged black holes with specific boundary conditions.

Findings

Partition function derived for charged black holes.

Analysis of Reissner-Nordstrom and BTZ black hole thermodynamics.

Inclusion of topological term in the action.

Abstract

We consider the most general diffeomorphism invariant action in 1+1 spacetime dimensions that contains a metric, dilaton and Abelian gauge field, and has at most second derivatives of the fields. Our action contains a topological term (linear in the Abelian field strength) that has not been considered in previous work. We impose boundary conditions appropriate for a charged black hole confined to a region bounded by a surface of fixed dilaton field and temperature. By making some simplifying assumptions about the quantum theory, the Hamiltonian partition function is obtained. This partition function is analyzed in some detail for the Reissner-Nordstrom black hole and for the rotating BTZ black hole.